Generating randomness from chaos and constructing chaos with desired randomness

We have designed, built and tested a switched-capacitor circuit for generating pseudo-random signals. the circuit is an electronic implementation of a one-dimensional discrete map, which has been fully understood mathematically. the time series of the circuit has extremely rich dynamics, e.g. aperiodicity, non-asymptoticity, ergodicity and fractal dimension. That is, the circuit is indeed chaotic. Furthermore, a general method for designing chaotic circuits with prescribed random properties is proposed. Numerous examples are given to illustrate the theory and methods developed in this paper.